The present invention relates to the blades in a turbo-machine. More specifically, the present invention relates to apparatus and methods for reducing vibration in the blades of a turbo-machine, such as a steam turbine, by employing vibration suppressing devices.
The steam flow path of an axial flow steam turbine is formed by a stationary cylinder and a rotor. A large number of stationary vanes are attached to the cylinder in a circumferential array and extend inward into the steam flow path. Similarly, a large number of rotating blades are attached to the rotor in a circumferential array and extend outward into the steam flow path. The stationary vanes and rotating blades are arranged in alternating rows so that a row of vanes and the immediately downstream row of blades form a stage. The vanes serve to direct the flow of steam so that it enters the downstream row of blades at the correct angle. The blade foils extract energy from the steam, thereby developing the power necessary to drive the rotor and the load attached to it.
During operation of a turbo-machine, the rotating blades are subject to oscillatory excitation at frequencies which coincide with integer multiples, referred to as harmonics, of the rotor rotational frequency. Such excitation is referred to as synchronous excitation. Synchronous blade excitation can be created by non-uniformities in the flow of the motive fluid (i.e., steam in the case of a steam turbine) that may vary in space around the circumference of the turbo-machine. Such non-uniformities result from the presence of (i) such features as extraction pipes and reinforcing ribs, and (ii) imperfections in the shape and spacing of the stationary vanes.
Thus, as a result of the oscillatory excitation, turbo-machine blades undergo vibratory deflections that create vibratory stresses in the blades. These vibratory stresses can result in high cycle fatigue cracking if their magnitude is not controlled. This problem is exacerbated by the fact that a turbo-machine blade typically has a number of resonant frequencies associated with its various vibratory modes;--i.e., tangential bending, axial bending, torsional, etc. If the oscillatory excitation to which the blade is subjected is close to one of its resonant frequencies, the vibratory stresses can quickly build up to destructive levels. To avoid this occurrence, in turbomachines with rotors that are intended to operate at, or very near to, a single rotational frequency, the designer attempts to design the larger rotating blades such that at least one, and preferably as many as possible, of the lower resonant frequencies do not coincide with harmonics of the rotor rotational frequency,--typically referred to as "tuning."
However, it is not always possible to predict and control a blade's resonant frequencies with sufficient accuracy to provide sufficient margin between each resonant frequency and the various rotor rotational harmonic frequencies. Also, many turbo-machines are required to operate at a variety of rotational speeds. Even in nominally fixed-speed turbine-generators, rotor harmonic frequencies can change due to under-frequency or over-frequency operation necessitated by electrical system requirements. Moreover, blades can exhibit substantial vibratory responses even at frequencies that are not coincident with harmonics of the rotor rotational frequency.
Hence, excessive vibratory stress can occur during operation. One approach utilized in the past to minimize the vibratory stress, in addition to strengthening the blade, has been to suppress blade vibration by connecting the foils of the blades together at one or more radial locations, thereby constraining deflections at these locations. Various approaches have been used in the past for connecting blade foils together, such as tip shrouds, welded lugs and tie wire. Tip shrouds have the advantage of providing aerodynamic benefits due to control of radial flow and the minimization of leakage past the blade row.
Unfortunately, if all of the blades in a row are coupled by a 360.degree. connection, the connecting device must change its circumferential length whenever its radial position is changed. As a result, the radial growth of the rotor at operating speeds can create stresses in the connecting device that can lead to failure. Traditionally, this problem has been avoided by using a number of connecting device segments, which divide the blades in the row into a number of groups. There are circumferential gaps at the ends of each connecting device segment that allow the connecting devices to accommodate radial growth of the rotor without excessive stresses.
One method of maximizing the effectiveness of the connecting device as a means for reducing vibration is to adjust its length so that the number of blades that the connecting device connects into a group is a function of the blade resonant frequency of concern. Often, this is the resonant frequency of first tangential vibratory mode because this mode can produce especially large resonant stresses and because connecting devices are especially effective in inhibiting vibrations in this mode. Specifically, the number of blades connected by the connecting device is equal to the number of blades in the row divided by the rotor rotational harmonic that is closest to the resonant frequency of the mode under consideration. Thus, if there are 120 blades in the row and the resonant frequency of the first tangential vibratory mode is closest to the 5th harmonic, then five connecting devices are used at each of one or more radial locations, with the length of each connecting device being such that it encompasses 24 blades (120/5=24). Such connecting devices are typically referred to as "harmonic" or "long-arc" and are disclosed in U.S. Pat. No. 3,588,278 (Ortolano), hereby incorporated by reference in its entirety.
However, as a consequence of centrifugal loading, the radius and circumference of the rotor increase with increasing speed, as do the radial locations of the various parts of the foils as well. As a result of the circumferential restraint provided by the harmonic restraints, the aforementioned radial growth can produce large tensile stresses in the harmonic restraints, and large bending stresses in the blade foils and roots. Because the effects of the circumferential restraint are cumulative from the center of the blade group, these stress effects are especially pronounced in and adjacent to the end blades of the groups. Moreover, because the tangential bending stiffness of long turbo-machine blades typically increases drastically as one approaches the base of the foil, these stress effects are typically greater for welded lugs or tie wires that are located away from the tips of the blades, than they are for shrouds that are located at the tips of the blades.
It is therefore desirable to provide a method and apparatus for suppressing blade vibration that provides substantial restraint against foil deflections while not subjecting the blades or the foil restraints to excessive steady stresses.
In some cases, harmonic shrouding has not been entirely effective in preventing blade vibratory failures. Harmonic shrouding does not increase the stiffness of the structure to the same extent as does a continuous 360.degree. structure. The increase in frequency associated with a 360.degree. coupling substantially raises the natural frequencies of all modes, and thus minimizes the number of such modes that can potentially interact with the lower harmonics of rotor rotational speed. Minimizing the number of such lower-harmonic modes is useful because such lower harmonics generally provide substantially greater magnitudes of excitations than do higher harmonics.
The use of a 360.degree. coupling also essentially eliminates responses to modes in which the blade motion is primarily tangential. This is accomplished by the cancellation of variations in tangential input energy around the entire circumference of the blade row.
Moreover, a 360.degree. coupling produces a structure that tends to respond substantially at a single natural frequency for each mode of vibration;--i.e., the frequency that is associated with a nodal-diameter pattern in the disk where the number of nodal diameters is equal to the number of the harmonic of running speed at which the vibration occurs. By contrast, multiply-grouped blades will respond over a range of frequencies because, as a practical matter, the natural frequency of each blade will vary as result of manufacturing variations. Under these conditions, the structure exhibits a primary response at the nodal-diameter pattern associated with the number of the harmonic of running speed. In addition, the structure exhibits various secondary responses associated with other nodal-diameter patterns. The phenomenon of multiple responses for each fundamental mode of the turbine blades is sometimes referred to as "mistuned bladed-disk response."
The range of frequencies for different nodal-diameter patterns of a single blade mode is much larger than the range of the individual natural frequencies of the individual blades or blade groups for that mode. Specifically, the range of the individual blade frequencies is ordinarily controlled to within a few Hz for each mode, but the range of nodal-diameter frequencies for a given mode often exceeds the amount by which the harmonics of rotor speed are separated (60 Hz in the case of a 3600-rpm turbo-machine). For this reason, it is virtually impossible to suppress response at all such frequencies by tuning.
The extent of this problem depends on the magnitude of the secondary responses. In the inventor's experience with multiply-grouped blades, it is not unusual to observe that the strongest of the secondary responses has a magnitude of one-third to one-half of the primary response. Such a magnitude can easily produce vibratory stresses that exceed the fatigue strength of the material. In such a case, the secondary as well as the primary mode must be tuned in order to ensure reliable operation. Tuning such a frequency is difficult at best. In tuning a primary frequency, the designer can make small changes to the foil design that result in relatively large changes in natural frequency. Unfortunately, the separations between the primary frequency and the various secondary frequencies are governed primarily by the flexibility characteristics of the turbine disc and are much more difficult to change substantially within the other constraints that are imposed on a turbine design. The designer is thus faced with the problem of ensuring that two or more natural frequencies will both fall between a single pair of harmonics of running speed, where the range of those natural frequencies is a substantial fraction of the separation between the successive harmonics of running speed.
Even a continuously-coupled structure of non-identical blades can exhibit secondary responses. But because the non-identical blades are more intimately connected to each other, the magnitude of the secondary response can be expected to be much smaller.
In the past, continuous 360.degree. rigid coupling has been achieved by connecting the trailing edge of one blade to the leading edge of the next, in a zig-zag fashion. This approach relies on the torsional flexibility of the blade in its upper portion. Unfortunately, when applied at only the blade tip, this approach is ineffective for long flexible blades, in which tip interconnection alone does not provide adequate stiffness.
Another approach utilizes downward-arched, thin, flexible shroud segments that are riveted through the tips of adjoining blades. When the circumference increases under centrifugal loading, these segments accommodate the required circumferential growth by becoming less arched. However, this approach tends to provide an undesirable interference with steam flow in the vicinity of the blade tip, and does not facilitate sealing against steam flow over the blade tips.
Still other approaches utilize various structures that permit sliding motion between adjoining blades or blade groups. Examples include sliding contact between the faces of shroud segments and/or lashing stubs, tabs fastened below one shroud segment and held by centrifugal force to the underside of the adjoining shroud segment, and sleeves that are placed around lashing stubs or lacing wires. All of these devices provide the additional (and frequently primary) benefit of introducing substantial damping into the structure. They all suffer from the disadvantage that wear can render them ineffective.
With respect to energy cancellation, harmonic grouping has been used to suppress response to a single harmonic of running speed. Unlike harmonic grouping, however, continuous 360.degree. coupling addresses all harmonics of running speed. This is especially important when the primary and substantial secondary responses for a given mode together span a range that is a substantial fraction of the separation between successive harmonics. Harmonic grouping can suppress response at only one of the adjoining harmonics, while continuous coupling can suppress response at both.
Therefore, it desirable to develop a vibration suppression device capable of providing substantially the benefits of a 360.degree. coupling without the problems associated with radial growth at operating speeds.